向量组的线性相关性的教学方法探讨
Discussion on the Teaching Method of Linear Dependence of Vector Group

向量组的线性相关性是线性代数课程最重要的内容之一，概念较为抽象和复杂，是线性代数教学中的重点和难点。本文从线性相关性的概念引入、判定方法以及思政元素三个方面，探讨了线性相关性的教学方法。通过融入矩阵思维和化归思想的方式，结合几何图形和思维导图等直观工具，启发并帮助学生更好地理解和掌握向量组线性相关性的概念，体会代数思想。
The linear dependence of vector group is one of the most important contents of linear algebra course. The concept is abstract and complex, which is the key and difficult point in the teaching of linear algebra. This paper discusses the teaching methods of linear dependence from three aspects: the introduction of the concept of linear dependence, the determination method and the ideological politic elements. Combined with intuitive tools such as geometric figures and mind maps, it integrates the idea of reduction and matrix thinking to help students better understand and master the concept of linear dependence of vector groups and experience algebraic ideas.